**TUESDAY: 5 December 2023. Afternoon Paper. Time Allowed: 2 hours.**

**This paper is made up of fifty (50) Multiple Choice Questions. Answer ALL questions by indicating the letter (A, B, C or D) that represents the correct answer. Each question is allocated two (2) marks.**

**1. What per cent of 80 is 12?**

A. 6.67%

B. 66.7%

C. 15%

D. 9.6% (2 marks)

**2. Convert the decimal number 3.98 to a percentage.**

A. 3.98%

B. 0.0398%

C. 39.8%

D. 398% (2 marks)

**3. Convert 75.20% into a decimal number.**

A. 0.752

B. 7.52

C. 75.2

D. 0.0752 (2 marks)

**8. Round off 7,510 to the nearest thousand.**

A. 7,500

B. 7,600

C. 7,000

D. 8,000 (2 marks)

**9. A ratio equivalent to 3:8 is.**

A. 3:11

B. 6:24

C. 9:24

D. 18:40 (2 marks)

**10. Two numbers are in the ratio 7:9. If the sum of the numbers is 112 then the larger number is.**

A. 49

B. 42

C. 63

D. 72 (2 marks)

**11. The ratio of 1.5m to 10cm is.**

A. 1:5

B. 15:10

C. 10:15

D. 15:1 (2 marks)

**12. The length and width of a rectangle are in the ratio 3:2. If the width of the rectangle is 28cm, then the length of the rectangle is?**

A. 18

B. 42

C. 70

D. 56 (2 marks)

**13. Three business partners, Mary, John and Peter share profits in the ratio of 3:3:4 respectively. If Peter received Sh.90,000. How much was the profit earned?**

A. Sh.36,000

B. Sh.54,000

C. Sh.225,000

D. Sh.200,000 (2 marks)

**14. Jane saves 2/5 of her salary in a SACCO every month. How much will she have saved in 9 months if she earns a monthly salary of Sh.40,000.**

A. Sh.16,000

B. Sh.24,000

C. Sh.144,000

D. Sh.214,000 (2 marks)

**23. Find a**

A. -2

B. 2

C. 5

D. 3 (2 marks)

**24. Find b**

A. -5

B. 2

C. 5

D. -6 (2 marks)

**25. Find the determinant of P **

A. 1

B. 0

C. -1

D. 5 (2 marks)

**28. The marked price of a book was Sh.500. The book was sold for Sh.450. What is the percentage discount offered on the product?**

A. 5%

B. 10%

C. 11%

D. 50% (2 marks)

**29. Dennis Juma bought a bike for Sh.7,500. He wants to sell it by making a profit of 25% on the selling price. What is the selling price of the bike?**

A. Sh.9,375

B. Sh.5,625

C. Sh.10,000

D. Sh.9,500 (2 marks)

**30. Rita Mueni sold apples for Sh.400. She made a profit of 25% on cost. Find the cost price of the apples.**

A. Sh.320

B. Sh.200

C. Sh.300

D. Sh.250 (2 marks)

**31. The student population of a college is increasing at the rate of 20% per annum. Calculate the student population after three years if the current population is 1,000.**

A. 1,200

B. 1,440

C. 1,728

D. 3,600 (2 marks)

**32. The production of a firm rose to 2,500 bags from 1,600 bags in two years. Find the rate of growth per annum.**

A. 25%

B. 20%

C. 200%

D. 250% (2 marks)

**33. Under the reducing balance method of providing for depreciation, the amount of depreciation _______________.**

A. Increases every year

B. Remains constant

C. Decreases every year

D. Increases or decreases every year (2 marks)

**34. Calculate the amount of interest earned if a sum of Sh.800,000 is invested for three years at a simple interest rate of 8% per annum.**

A. Sh.192,000

B. Sh.608,000

C. Sh.80,000

D. Sh.992,000 (2 marks)

**35. The cost of a motor vehicle in Britain is 30,500 British Pounds (£). Determine the cost of the motor vehicle in Kenya Shillings (KES) assuming the prevailing exchange rate is 1 British pound (£) = 132 KES.**

A. Sh.4,026,000

B. Sh.231.06

C. Sh.231,060.60

D. Sh.4,000,000 (2 marks)

**36. Lydia Njuguna bought a delivery van for Sh.2,800,000. The car depreciates at the rate of 14% per annum on a straight line basis. Calculate the value of the car after 2 years.**

A. Sh.2,016,000

B. Sh.784,000

C. Sh.2,000,000

D. Sh.2,006,000 (2 marks)

**37. The price of 1kg of cooking fat has increased by 20% over the last one month to retail at Sh.240 per kg. Calculate the retail price per kg before the price increases.**

A. Sh.160

B. Sh.200

C. Sh.300

D. Sh.280 (2 marks)

**38. ABC Ltd pays its employees on hourly basis. The normal rate per hour is Sh.200 while overtime is paid at the rate of 25% above the normal hourly rate. The normal working hours per week are 32 hours. Calculate the weekly wage for an employee who worked for 40 hours.**

A. Sh.6,400

B. Sh.8,000

C. Sh.8,400

D. Sh.10,000 (2 marks)

**39. Michael Oketch makes an initial investment of Sh.X at 10% compound interest in ABC bank. Calculate the value of X if at the end of 3 years the total amount in the investment account is Sh.85,184.**

A. Sh.59,628.80

B. Sh.60,000

C. Sh.64,000

D. Sh.76,665.60 (2 marks)

**40. What will be the amount to be paid at the end of three years on Sh.3,500 at an interest rate of 2% per annum compounded half-yearly?**

A. Sh.3,606.054

B. Sh.3,710

C. Sh.3,715.3205

D. Sh.3,714.228 (2 marks)

**41. The mean cost of 12 items is Sh.225. What is the cost of the 13th item that causes the mean to become Sh.250?**

A. Sh.250

B. Sh.237.5

C. Sh.550

D. Sh.475 (2 marks)

**42. Find the mean score.**

A. 30

B. 30.275

C. 31.04

D. 32 (2 marks)

**43. Find the median score.**

A. 27

B. 30

C. 34

D. 32 (2 marks)

**44. Find the standard deviation of the scores.**

A. 4.90

B. 5.23

C. 24

D. 27.32 (2 marks)

**Use the information below to answer Question 45 to Question 47.**

A box contains 4 blue balls and 6 red balls. A ball is drawn from the box and then replaced. A second ball is then drawn.

Find the probabilities that:

**48. Two events are said to be dependent if _______________________.**

A. They can happen together

B. They cannot happen together

C. The occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of the other event

D. The occurrence or non-occurrence of one event affects the occurrence or non-occurrence of the other

event (2 marks)

**49. The probability of one event happening is referred to as:**

A. Simple probability

B. Marginal probability

C. Joint probability

D. Equally likely event (2 marks)

**50. Determine the modal value in the following distribution:**

**2, 4, 7, 9, 3, 0, 5, 3, 1, 7, 9, 3**

A. 3

B. 7

C. 9

D. 2 (2 marks)